EspinS¶
Spin Hamiltonian¶
\[\begin{split}\mathcal{H}
=&
\underbrace{\sum_{i}\Delta_i\,(\hat{z}_i\cdot\mathbf{S}_i)^2}_{\text{single-ion term}}
+
\underbrace{\sum_{i}\mathbf{B}\cdot\mathbf{S}_i}_{\text{magnetic field}}
-\\&-
\underbrace{\frac{1}{2}\sum_{i,j}J_{ij}\,\mathbf{S}_i\cdot\mathbf{S}_j}_{\text{exchange term}}
+
\underbrace{\frac{1}{2}\sum_{i,j}\mathbf{D}_{ij}\cdot(\mathbf{S}_i\times\mathbf{S}_j)}_{\text{Dzyaloshinskii-Moriya term}}
+\\&+
\underbrace{\frac{1}{2}\sum_{i,j}B_{ij}\left(\mathbf{S}_i\cdot\mathbf{S}_j\right)^2}_{\text{bi-quadratic term}}\end{split}\]
Convention¶
Spin normalized |
no |
Multiple counting |
yes |